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(II) Dimensional analysis. Waves on the surface of the ocean do not depend significantly on the properties of water such as density or surface tension. The primary "return force" for water piled up in the wave crests is due to the gravitational attraction of the Earth. Thus the speed $v(\mathrm{m} / \mathrm{s})$ of ocean waves depends on the acceleration due to gravity $g .$ It is reasonable to expect that $v$ might also depend on water depth $h$ and the wave's wavelength $\lambda$ . Assume the wave speed is given by the functional form $v=C g^{\alpha} h^{\beta} \lambda^{\gamma},$ where $\alpha, \beta, \gamma,$ and $C$ are numbers without dimension. $(a)$ In deep water, the water deep below does not affect the motion of waves at the surface. Thus $v$ should be independent of depth $h$ (i.e., $\beta=0 ) .$ Using only dimensional analysis,determine the formula for the speed of surface waves in deep water. $(b)$ In shallow water, the speed of surface waves is found experimentally to be independent of the wavelength (i.e., $\gamma=0 ) .$ Using only dimensional analysis, determine the formula for the speed of waves in shallow water.

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a) $v=k \sqrt{g \gamma}$b) $v=k \sqrt{g h}$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 15

Wave Motion

Periodic Motion

Mechanical Waves

Electromagnetic Waves

Cornell University

University of Sheffield

McMaster University

Lectures

03:40

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength these are: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.

10:59

In physics, Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. They underpin all electric, optical and radio such electromagnetic technologies as power generation, electric motors, wireless communication, cameras, televisions, computers, and radar. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of these fields. The equations have two major variants. The microscopic Maxwell equations have universal applicability but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the atomic scale. The macroscopic Maxwell equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale details. The equations were published by Maxwell in his 1864 paper "A Dynamical Theory of the Electromagnetic Field". In the original paper Maxwell fully derived them from the Lorentz force law (without using the Lorentz transformation) and also from the conservation of energy and momentum.

05:43

(a) Shallow water is nondi…

So this question Introduce it very quartered scientific. Messer. That is a very sick shoulder to hip physics, especially for babies. It's researches, and this is quite a national analysis. So what would you do? That issue that assists is that here we want you know, what is a relationship? Oh, see, uh, of the speed off state of waves, it's the ocean, and helplessness depend on Portuguese. So we won't. Yes, that this is a speed way, cell service, emotion. It would be, I guess, us. It depends off the gravity G. It depends in some way. Thio. It's a depths off the water inch and probably also the waves breathless and whether it is just by thinking about it and I trying to pick up by camp toppers support your introduction and soon it might be some constant in front of it. And these could be square. Could YouTube Sewer has their own power. It just wasn't our for Vega because they don't know. So we're here. We will proceed because we knows included from beaches for V. So you did. It also is years. Is it? See is just a dimension iss constant G uh, this is SSA practitioner consideration was needed for City Square. Is it for H? White is leader. And, uh, let that is also, Peter. So here we have a tiny bit of difficulty already. See, because both the height, age and Linda, that's the unit leader. That phase that using official analysis, Beta and God, we cannot distinguish. Should have been a column because said both have disputed of Peter. So what can we do? That was a question. Made it easier for us because of prostrate relates to assumptions. Is this that 80 or well, you can't assume that worked deep down below says surface water little affect service motion. So 40 water, because soon is that he is independent of itch or other words. Data equals zero, and e shower is experimentally found to be independent of the weightless. So God like. So this helps us bring it two bounties because we only have what? Oddity these units off. Peter Data, six seconds. I'm cedar. Go. Okay. And now we can finally start to do the actual division of the Texas. So if we expense right inside, this is Peter, my foot. Just divided by a second or two as a descendant of Hester. Mitch. So this gives us sis. Yeah. So this gives us the relationships at our house. What's what? And to our FA we'll see is this tells us are far equals data this one off. So if we put this back here, get B, it wasn't Constance with Bush cake and its workers of G And since he here and here we look it Oh, ourselves equals he waas. Well, half. So here we have B Smoot of G. I'm ch So according to dimension that exists, we get sister nutrition for deep water and this relationship for shallow water.

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